Large N Duality for Compact Calabi-Yau Threefolds

We study geometric transitions for topological strings on compact Calabi-Yau hypersurfaces in toric varieties. Large N duality predicts an equivalence between topological open and closed string theories connected by an extremal transition. We develop new open string enumerative techniques and perform a high precision genus zero test of this conjecture for a certain class of toric extremal transitions. Our approach is based on a) an open string version of Gromov-Witten theory with convex obstruction bundle and b) an extension of Chern-Simons theory treating the framing as a formal variable.